If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\). Find A\(^T\) + B, ( where T means transpose)
A
\(\begin{pmatrix}4 & 8\\3 & 2\\4 & 1\end{pmatrix}\)
B
\(\begin{pmatrix}4 & -8\\3 & 2\\4 & 1\end{pmatrix}\)
C
\(\begin{pmatrix}4 & 8\\4 & -2\\3 & 1\end{pmatrix}\)
D
\(\begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Given that A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\)
A\(^T\) = \(\begin{pmatrix}3 & 4\\2 & 2\\1 & -1\end{pmatrix}\)
Find A\(^T\) + B = \(\begin{pmatrix}3 & 4\\2 & 2\\1 & -1\end{pmatrix}\) + \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\) = \(\begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70344)